Abstract: In this paper, we present some new upper bounds for
the spectral radius of iterative matrices based on the concept of
doubly α diagonally dominant matrix. And subsequently, we give
two examples to show that our results are better than the earlier ones.
Abstract: Estimating the reliability of a computer network has been a subject of great interest. It is a well known fact that this problem is NP-hard. In this paper we present a very efficient combinatorial approach for Monte Carlo reliability estimation of a network with unreliable nodes and unreliable edges. Its core is the computation of some network combinatorial invariants. These invariants, once computed, directly provide pure and simple framework for computation of network reliability. As a specific case of this approach we obtain tight lower and upper bounds for distributed network reliability (the so called residual connectedness reliability). We also present some simulation results.
Abstract: In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
Abstract: The Merrifield-Simmons index of a graph G is defined as the total number of its independent sets. A (n, n + 2)-graph is a connected simple graph with n vertices and n + 2 edges. In this paper we characterize the (n, n+2)-graph with the largest Merrifield- Simmons index. We show that its Merrifield-Simmons index i.e. the upper bound of the Merrifield-Simmons index of the (n, n+2)-graphs is 9 × 2n-5 +1 for n ≥ 5.
Abstract: For the sensor network to operate successfully, the active nodes should maintain both sensing coverage and network connectivity. Furthermore, scheduling sleep intervals plays critical role for energy efficiency of wireless sensor networks. Traditional methods for sensor scheduling use either sensing coverage or network connectivity, but rarely both. In this paper, we use random scheduling for sensing coverage and then turn on extra sensor nodes, if necessary, for network connectivity. Simulation results have demonstrated that the number of extra nodes that is on with upper bound of around 9%, is small compared to the total number of deployed sensor nodes. Thus energy consumption for switching on extra sensor node is small.
Abstract: Stable bacterial polymorphism on a single limiting resource may appear if between the evolved strains metabolic interactions take place that allow the exchange of essential nutrients [8]. Towards an attempt to predict the possible outcome of longrunning evolution experiments, a network based on the metabolic capabilities of homogeneous populations of every single gene knockout strain (nodes) of the bacterium E. coli is reconstructed. Potential metabolic interactions (edges) are allowed only between strains of different metabolic capabilities. Bacterial communities are determined by finding cliques in this network. Growth of the emerged hypothetical bacterial communities is simulated by extending the metabolic flux balance analysis model of Varma et al [2] to embody heterogeneous cell population growth in a mutual environment. Results from aerobic growth on 10 different carbon sources are presented. The upper bounds of the diversity that can emerge from single-cloned populations of E. coli such as the number of strains that appears to metabolically differ from most strains (highly connected nodes), the maximum clique size as well as the number of all the possible communities are determined. Certain single gene deletions are identified to consistently participate in our hypothetical bacterial communities under most environmental conditions implying a pattern of growth-condition- invariant strains with similar metabolic effects. Moreover, evaluation of all the hypothetical bacterial communities under growth on pyruvate reveals heterogeneous populations that can exhibit superior growth performance when compared to the performance of the homogeneous wild-type population.
Abstract: Many multimedia communication applications require a
source to transmit messages to multiple destinations subject to quality
of service (QoS) delay constraint. To support delay constrained
multicast communications, computer networks need to guarantee an
upper bound end-to-end delay from the source node to each of
the destination nodes. This is known as multicast delay problem.
On the other hand, if the same message fails to arrive at each
destination node at the same time, there may arise inconsistency and
unfairness problem among users. This is related to multicast delayvariation
problem. The problem to find a minimum cost multicast
tree with delay and delay-variation constraints has been proven to
be NP-Complete. In this paper, we propose an efficient heuristic
algorithm, namely, Economic Delay and Delay-Variation Bounded
Multicast (EDVBM) algorithm, based on a novel heuristic function,
to construct an economic delay and delay-variation bounded multicast
tree. A noteworthy feature of this algorithm is that it has very high
probability of finding the optimal solution in polynomial time with
low computational complexity.
Abstract: A perfect secret-sharing scheme is a method to distribute a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of participants in any unqualified subset is statistically independent of the secret. The collection of all qualified subsets is called the access structure of the perfect secret-sharing scheme. In a graph-based access structure, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme realizing the access structure based on G is defined as AR = (Pv2V (G) H(v))/(|V (G)|H(s)), where s is the secret and v is the share of v, both are random variables from and H is the Shannon entropy. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing a given access structure is called the optimal average information ratio of that access structure. Most known results about the optimal average information ratio give upper bounds or lower bounds on it. In this present structures based on bipartite graphs and determine the exact values of the optimal average information ratio of some infinite classes of them.
Abstract: The weighting exponent m is called the fuzzifier that
can have influence on the clustering performance of fuzzy c-means
(FCM) and mÎ[1.5,2.5] is suggested by Pal and Bezdek [13]. In this
paper, we will discuss the robust properties of FCM and show that the
parameter m will have influence on the robustness of FCM. According
to our analysis, we find that a large m value will make FCM more
robust to noise and outliers. However, if m is larger than the theoretical
upper bound proposed by Yu et al. [14], the sample mean will become
the unique optimizer. Here, we suggest to implement the FCM
algorithm with mÎ[1.5,4] under the restriction when m is smaller
than the theoretical upper bound.
Abstract: This paper proves that the problem of finding connected
vertex cover in a 2-connected planar graph ( CVC-2 ) with maximum degree 4 is NP-complete. The motivation for proving this result is to
give a shorter and simpler proof of NP-Completeness of TRA-MLC (the Top Right Access point Minimum-Length Corridor) problem [1], by finding the reduction from CVC-2. TRA-MLC has many applications in laying optical fibre cables for data communication and electrical wiring in floor plans.The problem of finding connected vertex cover in any planar graph ( CVC ) with maximum degree 4 is NP-complete [2]. We first show that CVC-2 belongs to NP and then we find a polynomial reduction from CVC to CVC-2. Let a graph G0 and an integer K form an instance of CVC, where G0 is a planar graph and K is an upper bound on the size of the connected vertex cover in G0. We construct a 2-connected planar graph, say G, by identifying the blocks and cut vertices of G0, and then finding the planar representation of all the blocks of G0, leading to a plane graph G1. We replace the cut vertices with cycles in such a way that the resultant graph G is a 2-connected planar graph with maximum
degree 4. We consider L = K -2t+3 t i=1 di where t is the number of cut vertices in G1 and di is the number of blocks for which ith cut vertex is common. We prove that G will have a connected vertex
cover with size less than or equal to L if and only if G0 has a connected vertex cover of size less than or equal to K.
Abstract: In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.
Abstract: we propose a new normalized LMS (NLMS) algorithm, which gives satisfactory performance in certain applications in comaprison with con-ventional NLMS recursion. This new algorithm can be treated as a block based simplification of NLMS algorithm with significantly reduced number of multi¬ply and accumulate as well as division operations. It is also shown that such a recursion can be easily implemented in block floating point (BFP) arithmetic, treating the implementational issues much efficiently. In particular, the core challenges of a BFP realization to such adaptive filters are mainly considered in this regard. A global upper bound on the step size control parameter of the new algorithm due to BFP implementation is also proposed to prevent overflow in filtering as well as weight updating operations jointly.
Abstract: Given a parallel program to be executed on a heterogeneous
computing system, the overall execution time of the program
is determined by a schedule. In this paper, we analyze the worst-case
performance of the list scheduling algorithm for scheduling tasks
of a parallel program in a mixed-machine heterogeneous computing
system such that the total execution time of the program is minimized.
We prove tight lower and upper bounds for the worst-case
performance ratio of the list scheduling algorithm. We also examine
the average-case performance of the list scheduling algorithm. Our
experimental data reveal that the average-case performance of the list
scheduling algorithm is much better than the worst-case performance
and is very close to optimal, except for large systems with large
heterogeneity. Thus, the list scheduling algorithm is very useful in
real applications.
Abstract: The solution algorithm, based on Lagrangian relaxation, a sub-gradient method and a heuristic to find the upper bound of the solution, is proposed to solve the coordinated fleet routing and flight scheduling problems. Numerical tests are performed to evaluate the proposed algorithm using real operating data from two Taiwan airlines. The test results indicate that the solution algorithm is a significant improvement over those obtained with CPLEX, consequently they could be useful for allied airlines to solve coordinated fleet routing and flight scheduling problems.
Abstract: The plastic flow of metal in the extrusion process is
an important factor in controlling the mechanical properties of the
extruded products. It is, however, difficult to predict the metal flow
in three dimensional extrusions of sections due to the involvement of
re-entrant corners. The present study is to find an upper bound
solution for the extrusion of triangular sectioned through taper dies
from round sectioned billet. A discontinuous kinematically
admissible velocity field (KAVF) is proposed. From the proposed
KAVF, the upper bound solution on non-dimensional extrusion
pressure is determined with respect to the chosen process parameters.
The theoretical results are compared with experimental results to
check the validity of the proposed velocity field. An extrusion setup
is designed and fabricated for the said purpose, and all extrusions are
carried out using circular billets. Experiments are carried out with
commercially available lead at room temperature.
Abstract: The Chinese Postman Problem (CPP) is one of the
classical problems in graph theory and is applicable in a wide range
of fields. With the rapid development of hybrid systems and model
based testing, Chinese Postman Problem with Time Dependent Travel
Times (CPPTDT) becomes more realistic than the classical problems.
In the literature, we have proposed the first integer programming
formulation for the CPPTDT problem, namely, circuit formulation,
based on which some polyhedral results are investigated and a cutting
plane algorithm is also designed. However, there exists a main drawback:
the circuit formulation is only available for solving the special
instances with all circuits passing through the origin. Therefore, this
paper proposes a new integer programming formulation for solving
all the general instances of CPPTDT. Moreover, the size of the circuit
formulation is too large, which is reduced dramatically here. Thus, it
is possible to design more efficient algorithm for solving the CPPTDT
in the future research.
Abstract: Two constructions of unit-memory binary convolutional
codes from linear block codes over the finite semi-local ring F2r +vF2r , where v2 = v, are presented. In both cases, if the linear block code is systematic, then the resulting convolutional encoder
is systematic, minimal, basic and non-catastrophic. The Hamming
free distance of the convolutional code is bounded below by the
minimum Hamming distance of the block code. New examples of
binary convolutional codes that meet the Heller upper bound for
systematic codes are given.
Abstract: Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.
Abstract: In this paper, at first we explain about negative
hypergeometric distribution and its properties. Then we use the w-function
and the Stein identity to give a result on the poisson
approximation to the negative hypergeometric distribution in terms of the total variation distance between the negative hypergeometric and
poisson distributions and its upper bound.
Abstract: Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated.Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds for the moduli of the zeros of complex polynomials. That means, we provide disks in the complex plane where all zeros of a complex polynomial are situated. Such bounds are extremely useful for obtaining a priori assertations regarding the location of zeros of polynomials. Based on the proven bounds and a test set of polynomials, we present an experimental study to examine which bound is optimal.